Edit: See also https://whyafricanlanguages.org/2019/01/28/sequoyahs-ghost-a...
But after knowing writing was possible it just took a single determined individual, such as Sequoyah, to create a writing system for a language previously only spoken.
See also: https://en.wikipedia.org/wiki/Egg_of_Columbus
"When asked, “How could you possibly have done the first interactive graphics program, the first non-procedural programming language, the first object oriented software system, all in one year?” Ivan replied: “Well, I didn’t know it was hard.” (Alan Kay, Doing with Images Makes Symbols, 1987)"
He was tasked with finding a way of frosting light bulbs from the inside, without making them too brittle. Not being aware his assignment was a type of joke, he went about the task as if it was something that could be done and had been done before. The first electric light bulb frosted on the inside with sufficient strength for ordinary handling that could be sold to the public was invented by Pipkin in 1925.
Huh, it turns out his solution was acid etching the inside of the bulb, which was what I assumed they tried that didn't work.
Actually, he didn't. He knew that the Americans had a writing system that was sparse in its use of characters, and that it was capable of reflecting all text, but he didn't know any of the actual principles. This is why he created a syllabary (each character is roughly a syllable ) instead of an alphabet (each character is a phoneme). He also had access to an English-language Bible, although he couldn't read it--this is why Cherokee has several characters that look like Latin letters but have completely different pronunciation (ᏣᎳᎩ is pronounced "tsalagi").
The creation of the syllabary also corroborates the general history of scripts: most scripts start out as logographic, morph into a rebus phase (homophonic punning--using a picture of an eye to represent "I" because they sound the same), and then transition into a syllabary. In the development of Egyptian, the script instead became an abjad (reflecting only consonants); by the time this came to the Greeks, they added vowel letters to make the first alphabet (and all alphabets are essentially derived from the Greeks); the abugida innovation (marking vowels systematically) happened a few times, although most existing abugidas derive ultimately from the Brahmi script. Sequoyah skipped straight to a syllabary because of access to Latin script that illustrated that logographic script wasn't necessary.
 Mapping are of course rough in all forms of scripts, but syllabaries are usually even rougher to map, since languages can have quite complex consonant clusters. In practice, most such scripts tend to stick to classifying CV (consonant-vowel) pairs as syllables and use multiple characters to represent CVC, CCVC, CVCC, etc. syllables.
The only thing I do remember is having a book with the portrait by Henry Inman in it https://npg.si.edu/blog/portrait-sequoyah-henry-inman I still remember that portrait, and sitting around daydreaming that I was him.